It's software - just about everything is possible if you care to implement it. But there's no ready-made library to convert PDF to Word, certainly none that is free or open source. PDFs are for viewing and printing, not editing.

If you are prepared to spend a lot of work on this then you can use the PDF-interpreting code of the PDF-Renderer library and join that with the DOC/DOCX-generating capabilities of the Apache POI library.